Major Work
of
High School
Geometry and Algebra II
Common Core State Standards for Mathematics: Grade Level Emphases
North Carolina Department of Public Instruction
Page 1
Math Content Emphases
Content Emphases by Cluster describes content emphases in the standards at the cluster level for each
grade or course. These are provided because curriculum, instruction and assessment at each grade must reflect
the focus and emphasis of the standards.
Not all of the content in a given grade or course is emphasized equally in the standards. The list of
content standards for each grade or course is not a flat, one-dimensional checklist; this is by design. There are
sometimes strong differences of emphasis even within a single domain. Some clusters require greater emphasis
than others based on the depth of the ideas, the time they take to master, and/or their importance to future
mathematics or the demands of college and career readiness. An intense focus on the most critical material at
each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice.
Without such focus, attention to the practices would be difficult and unrealistic, as would best practices such as
formative assessment.
Saying that some things have greater emphasis is not to say that anything in the standards can safely be
neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave
students unprepared for the challenges of a later grade. Assessments will be designed with a much greater
proportion drawn from clusters designated as major and the remainder drawn from clusters designated as
additional/supporting, with these items placing emphasis on the major work of the grade or course.
Therefore, to make relative emphases in the standards more transparent and useful, this document
designates clusters as Major or Supporting/Additional for the grade or course in question. The following are
some recommendations for using the cluster-level emphases:
Do …
 Use the identified work to inform instructional decisions regarding time and other resources spent on
clusters of varying degrees of emphasis.
 Evaluate instructional materials taking the cluster-level emphases into account. The major work of the grade
must be presented with the highest possible quality; the supporting and additional work of the grade should
support the major focus, not detract from it.
 Allow the focus on the major work of the grade to open up the time and space to bring the Standards for
Mathematical Practice to life in mathematics instruction through sense-making, reasoning, arguing and
critiquing, modeling, etc.
 Set priorities for other implementation efforts taking the emphases into account, such as staff development;
new curriculum development; or revision of existing district or school level assessments.
Don’t …
 Neglect any material in the standards. (Instead, connect the Supporting/Additional Clusters to the other
work of the grade or course.)
 Sort clusters from Major to Supporting/Additional, and then teach them in that order. To do so would strip
the coherence and progressiveness of the mathematical ideas and miss the opportunity to enhance the major
work of the grade with the supporting/additional clusters.
 Use the cluster headings as a replacement for the standards or use the standards without the cluster heading.
All features of the standards matter because a focus is given at the cluster level as a way to talk about the
content with the necessary specificity, without going so far into detail as to compromise the coherence of the
standards.
Adapted from: http://engageny.org/resource/math-content-emphases/
Common Core State Standards for Mathematics: Grade Level Emphases
North Carolina Department of Public Instruction
Page 2
Major Work of Geometry
High School
Major Clusters
Quantities

Reason quantitatively and use units to
solve problems.
Congruence

Prove geometric theorems.
Similarity, Right Triangles, and
Trigonometry

Define trigonometric ratios and solve
problems involving right triangles.
Expressing Geometric Properties with
Equations

Use coordinates to prove simple
geometric theorems algebraically.
Modeling with Geometry
 Apply geometric concepts in modeling
situations.
Supporting/Additional Clusters
Congruence

Experiment with transformations in the
plane.
 Understand congruence in terms of
rigid motions.
 Make geometric constructions. Similarity, Right Triangles, and
Trigonometry
 Understand similarity in terms of


similarity transformations.
Prove theorems involving similarity.
Apply trigonometry to general
triangles.
Circles
 Understand and apply theorems about
circles.
 Find arc lengths and areas of sectors of
circles. Expressing Geometric Properties with
Equations
 Translate between the geometric
description and the equation for a
conic section. (Here because of circles.)
Geometric Measurement and
Dimension

Visualize relationships between
two‐dimensional and
three‐dimensional objects.
Common Core State Standards for Mathematics: Grade Level Emphases
North Carolina Department of Public Instruction
Page 3
Conditional Probability and the Rules
of Probability


Understand independence and
conditional probability and use them
to interpret data.
Use the rules of probability to compute
probabilities of compound events in a
uniform probability model.
Using Probability to Make Decisions
 Use probability to evaluate outcomes
of decisions.
Common Core State Standards for Mathematics: Grade Level Emphases
North Carolina Department of Public Instruction
Page 4
Major Work of Algebra II
High School
Major Clusters
The Real Number System
 Extend the properties of exponents to
Supporting/Additional Clusters
The Real Number System

rational exponents.
Quantities

Reason quantitatively and use units to
solve problems.
The Complex Number System


Seeing the Structure in Expressions


Interpret the structure of expressions.
Write expressions in equivalent forms
to solve problems. Arithmetic with Polynomials and
Rational Expressions

Understand the relationship between
zeros and factors of polynomials.
Creating Equations

Create equations that describe
numbers or relationships.
Reasoning with Equations and
Inequalities


Understand solving equations as a
process of reasoning and explain the
reasoning.
Represent and solve equations and
inequalities graphically.
Use properties of rational and
irrational numbers.
Perform arithmetic operations with
complex numbers.
Use complex numbers in polynomial
identities and equations.
Arithmetic with Polynomials and
Rational Expressions



Perform arithmetic operations on
polynomials.
Use polynomial identities to solve
problems.
Rewrite rational expressions.
Reasoning with Equations and
Inequalities


Solve equations and inequalities in one
variable.
Solve systems of equations.
Building Functions

Build new functions from existing
functions.
Trigonometric Functions



Extend the domain of trigonometric
functions using the unit circle.
Model periodic phenomena with
trigonometric functions.
Prove and apply trigonometric
identities.
Common Core State Standards for Mathematics: Grade Level Emphases
North Carolina Department of Public Instruction
Page 5
Interpreting Functions



Understand the concept of a function
and understand function notation.
Interpret functions that arise in
applications in terms of the context.
Analyze functions using different
representations. Making Inferences and Justifying
Conclusions

Understand and evaluate random
processes underlying statistical
experiments.
Building Functions
 Build a function that models a
relationship between two quantities.
Linear, Quadratic and Exponential
Models

Construct and compare linear,
quadratic, and exponential models and
solve problems.
Interpreting Categorical and
Quantitative Data

Summarize, represent, and interpret
data on a single count or measurement
variable.
Making Inferences and Justifying
Conclusions

Make inferences and justify
conclusions from sample surveys,
experiments, and observational
studies.
Common Core State Standards for Mathematics: Grade Level Emphases
North Carolina Department of Public Instruction
Page 6